Abstract

In survey sample inference, there are two fundamental positions that
can be taken with respect to randomized designs and the use of design
weights (inverses of selection probabilities): (1) both are necessary;
(2) neither is necessary. Indeed, neither is necessary, and there are
occasions when insistence on their use undermines inference. There are
other occasions when, the analyst being at a remove from the sampling
process, the selection probabilities are helpful information, which it
makes sense to incorporate into the method of inference. Strict maximum
likelihood inference (as distinguished from the pseudo-likelihood or
weighted distribution likelihood approaches) can suitably incorporate
the sample weights. The theory of this is not simple, but the practice
usually is. We illustrate these points.